Compare the amount of deaths in boxing (1,465 according to one study) and compare the amount of deaths in sanctioned MMA (two).
What about the little gloves?
Boxing gloves are meant to protect the hand, not the head, so really it's not much safer in that sense.
Also, the rules of boxing guarantee repeated head trauma. If a boxer is knocked down, he has 10 seconds to get up only to get pummeled again.
In MMA, if a fighter loses consciousness the fight is stopped and he doesn't have to suffer another knock down.
Repeated damage to the head adds up. Look at boxers later in their lives and careers and look at MMA fighters. Boxers slur and can barely be understood, MMA fighters don't have such problems.
Also, the addition of submission holds make the sport safer. In boxing, it's guaranteed that you're going to take many, many punches to the head. In MMA, this isn't always the case.
One fighter could take another down and submit him. If the fighter taps out, the fight is over and both men can walk away without a scratch.